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When a liquid is heated in a container, both expand. What we observe (apparent expansion) is less than the actual (real expansion): $\gamma_{\text{apparent}} = \gamma_{\text{real}} - \gamma_{\text{container}} = \gamma_{\text{real}} - 3\alpha_{\text{container}}$.

Mercury in glass: $\gamma_{\text{Hg}} = 1.82 \times 10^{-4}$ K$^{-1}$, $3\alpha_{\text{glass}} \approx 2.7 \times 10^{-5}$K$^{-1}$. Apparent expansion$\approx 1.55 \times 10^{-4}$K$^{-1}$.

Overflow from a full flask: $V_{\text{overflow}} = V_0(\gamma_{\text{liquid}} - 3\alpha_{\text{container}})\Delta T$.

For accurate liquid expansion measurements, use fused quartz containers ($\alpha \approx 0.5 \times 10^{-6}$), minimizing the container correction. Mercury thermometers work on apparent expansion — the mercury in the glass tube rises because mercury expands more than glass.$